Principles and psychophysics of Active Inference

Laurent Perrinet, Chloé Pasturel and Anna Montagnini

Probabilities and Optimal Inference to Understand the Brain

* (AUTHOR) Hi, I am Laurent Perrinet from (LOGO) the Institute de Neurosciences de la Timone in Marseille, a joint unit from the CNRS and AMU. Using computational models, I am investigating the link between the efficiency of behavioural responses in vision, their underlying neural code and their adaptation to the structure of the world.

* (SHOW TITLE - THEME) = In particular, I will use today a visual illusion -the FLE- to provide evidence that we use predictive mechanism to compensate for neural delays and perceive the visual world in **real-time** (I will try to define today what I mean by that...)

* (ACKNO) this endeavour involves different techniques, tools and... persons. From the head on, I wish to thank the people who collaborated to this project and in particular Rick Adams and Karl Friston and the Wellcome Trust Centre for Neuroimaging for providing the tools for a successful visit / but also Mina, Guillaume and Anna for the great oppportunity to link  theories with psychophysical data; Wahiba, Giacomo and Frédéric for the challenging task of linking such models to the neural activity in NHP, and finally Jean-Bernard, Sohir and Laurent Madelain for their essential knowledge in adaptation and reinforcement.

http://invibe.net/LaurentPerrinet/Presentations/2018-04-05_BCP_talk

Principles and psychophysics of Active Inference

Laurent Perrinet, Chloé Pasturel and Anna Montagnini

Probabilities and Optimal Inference to Understand the Brain

Outline

A dynamic probabilistic bias in visual motion direction

Raw psychophysical results

The Bayesian Changepoint Detector

Results using the BCP

A dynamic probabilistic bias in visual motion direction

Outline

A dynamic probabilistic bias in visual motion direction

Raw psychophysical results

The Bayesian Changepoint Detector

Results using the BCP

Raw psychophysical results

Outline

A dynamic probabilistic bias in visual motion direction

Raw psychophysical results

The Bayesian Changepoint Detector

Results using the BCP

The Bayesian Changepoint Detector

Bayesian Changepoint Detector

Initialize

$P(r_0)= S(r)$ or $P(r_0=0)=1$ and
$ν^{(0)}_1 = ν_{prior}$ and $χ^{(0)}_1 = χ_{prior}$

Observe New Datum $x_t$
Evaluate Predictive Probability $π_{1:t} = P(x |ν^{(r)}_t,χ^{(r)}_t)$
Calculate Growth Probabilities $P(r_t=r_{t-1}+1, x_{1:t}) = P(r_{t-1}, x_{1:t-1}) π^{(r)}_t (1−H(r^{(r)}_{t-1}))$
Calculate Changepoint Probabilities $P(r_t=0, x_{1:t})= \sum_{r_{t-1}} P(r_{t-1}, x_{1:t-1}) π^{(r)}_t H(r^{(r)}_{t-1})$
Calculate Evidence $P(x_{1:t}) = \sum_{r_{t-1}} P (r_t, x_{1:t})$
Determine Run Length Distribution $P (r_t | x_{1:t}) = P (r_t, x_{1:t})/P (x_{1:t}) $
Update Sufficient Statistics :

$ν^{(0)}_{t+1} = ν_{prior}$, $χ^{(0)}_{t+1} = χ_{prior}$
$ν^{(r+1)}_{t+1} = ν^{(r)}_{t} +1$, $χ^{(r+1)}_{t+1} = χ^{(r)}_{t} + u(x_t)$

Perform Prediction $P (x_{t+1} | x_{1:t}) = P (x_{t+1}|x_{1:t} , r_t) P (r_t|x_{1:t})$
go to (2)

The Bayesian Changepoint Detector

Outline

A dynamic probabilistic bias in visual motion direction

Raw psychophysical results

The Bayesian Changepoint Detector

Results using the BCP

Principles and psychophysics of Active Inference

Laurent Perrinet, Chloé Pasturel and Anna Montagnini

Probabilities and Optimal Inference to Understand the Brain